Application of He's homotopy and perturbation method to solve heat transfer equations: A python approach

•Homotopy and Perturbation method has been used to solve heat transfer equations.•Both linear and nonlinear differential equations are solved.•Python programming has been used to solve the problem.•Developed python code has been presented.•The results of computer program are in very good agreement w...

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Veröffentlicht in:Advances in engineering software (1992) Jg. 170; S. 103160
Hauptverfasser: Dumka, Pankaj, Pawar, Parth Singh, Sauda, Abhay, Shukla, Gaurav, Mishra, Dhananjay R.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.08.2022
Schlagworte:
Heat transfer
Homotopy and perturbation method (HPM)
Nonlinear differential equations
Python
SymPy
HPM
Nonlinear differential equations
LSM
Homotopy and perturbation method (HPM)
WRMs
SymPy
ADM
VIM
Heat transfer
Python
ISSN:0965-9978
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Zusammenfassung:•Homotopy and Perturbation method has been used to solve heat transfer equations.•Both linear and nonlinear differential equations are solved.•Python programming has been used to solve the problem.•Developed python code has been presented.•The results of computer program are in very good agreement with the analytical results. In this research article, an attempt has been made to solve the linear/nonlinear and steady/unsteady heat transfer equations using the Homotopy and Perturbation method (HPM). Moreover, the implementation of HPM has been done by using SymPy, a library in python, to solve problems symbolically. Total three problems were dealt viz. steady-state conduction with heat generation, lumped capacitance analysis with a variable specific heat of the material, and heat transfer in uniform rectangular fin with radiation from the surface. In all the cases, the HPM has given excellent results compared to the analytical and numerical. Finally, the execution of SymPy has been explained, and a detailed procedure to implement HPM through python has been presented for all three cases.
ISSN:0965-9978
DOI:10.1016/j.advengsoft.2022.103160